1. Field of the Invention
The invention relates to a device for calculating differences between coordinates of two particles.
2. Description of the Related Art
The field in which the behavior of a liquid, a solid, or a polymer is supposed as a result of motions of atoms constituting the substance and the motions are studied by simulating them through a computer is called molecular dynamics. In molecular dynamics, atoms or molecules are considered as particles. Forces acting between these particles are calculated, and positions where the particles are located after an elapse of time are calculated. These calculations are repeated to obtain the loci of the particles. On the basis of the obtained loci, the property, and the like of the substance are determined. In molecular dynamics, therefore, forces acting between particles are physical quantities which must be calculated.
A force acting on an i-th particle is a sum total of forces which are exerted by all particles other than the i-th particle onto the i-th particle. Since a force acting between two particles depends on the distance between the particles, it is first required to obtain the distance between the particles. When coordinates of the i-th particle are indicated by (x.sub.i, y.sub.i, z.sub.i) and coordinates of a j-th particle are indicated by (x.sub.j, y.sub.j, z.sub.j), the particle distance r.sub.j is obtained as follows: EQU r.sub.j ={(.DELTA.x.sub.j).sup.2 +(.DELTA.y.sub.j).sup.2 +(.DELTA.z.sub.j).sup.2 }.sup.1/2 EQU .DELTA.x.sub.j =x.sub.j -x.sub.i EQU .DELTA.y.sub.j =y.sub.j -y.sub.i EQU .DELTA.z.sub.j =z.sub.j -z.sub.i
A system in which differences are calculated by subtracting coordinates of an i-th particle from coordinates of an interested j-th particle, is known such as a difference calculating device disclosed in FASTRUN: "A Special Purpose, Hardwired Computer for Molecular Simulation", PROTEINS: Structure, Function, and Genetics 11: pp. 242-253 (1991). However, this literature teaches only that a host computer produces a pair of the interested j-th particle and the i-th particle.
However pressure, as an external force, acts on a substance. When the pressure is changed, positions of particles in the substance may be changed. When a temperature of the substance is changed, the pressure or volume of the substance may be changed. A volume change means a positional change of particles. Accordingly, for calculations in molecular dynamics, a situation where the pressure must be obtained occurs frequently. Regarding this point, the calculating device, as disclosed in the above-mentioned literature, can obtain force and energy in accordance with the pair of particles, but cannot obtain force and pressure.
Since an actual substance includes a great number (in the order of the Avogadro's number or 10.sup.23) of atoms, the computational complexity becomes so enormous that it is impossible to conduct a computer simulation using these great number of atoms as they are.
In order to comply with this, a boundary of a virtual rectangular parallelepiped is assumed in a substance, as shown in FIG. 3, and only motions of particles inside the boundary are calculated. The respective sides of the rectangular parallelepiped are determined so that the following conditions are satisfied. At first, the particle density in the rectangular parallelepiped is made equal to that of the actual substance. Next, when the distance between two particles is greater than a specific value r.sub.c, it is assumed that the force acting between the particles can be neglected, and that 2r.sub.c is smaller than L.sub.x, L.sub.y, L.sub.z (or 2r.sub.c &lt;L.sub.x, L.sub.y, L.sub.z). Finally, it is assumed that the actual substance can be constructed by arranging the same parallelepipeds as the above-mentioned rectangular parallelepiped in lateral and longitudinal directions. When the substance is a crystal, for example, the lengths of the sides are determined on the basis of the lattice constant. The thus determined rectangular parallelepiped is called the periodic boundary condition.
In the periodic boundary condition, it is assumed that, in the rectangular parallelepipeds surrounding and equivalent to the original rectangular parallelepiped, atoms are arranged in the exactly same configuration as that of the original rectangular parallelepiped. This is two-dimensionally illustrated in FIG. 4. Specifically, with respect to particle j.sub.0 of the original rectangular parallelepiped, particles j.sub.1 to j.sub.8 surround particle j.sub.0. When a force which is exerted by particle j onto particle i is to be calculated, only one among particles j.sub.0 to j.sub.8 which is nearest to particle i is required to be considered, because 2r.sub.c &lt;L.sub.x, L.sub.y, L.sub.z and hence it is possible for only one of particles j.sub.0 to j.sub.8 to be separated from particle i by a distance shorter than r.sub.c.
Actually, as shown in FIG. 5, the number of rectangular parallelepipeds surrounding the original rectangular parallelepiped is 26. Therefore, it is required that the particle which is nearest to particle i is selected from particle, and 26 reflected images of the particle j and the difference between coordinates of the selected one and those of particle i is obtained. Generally, the process of obtaining such a difference by software requires enormous calculations, thereby producing a problem in calculation speed. However, no attempt has been made to solve the periodic boundary condition by a hardware approach.